Geodesic
The problem on small motions of a mixture of viscous compressible fluids
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 20 (2023) no. 2, pp. 1552-1589

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In this paper, we study the problem on small motions and normal oscillations of a homogeneous mixture of several viscous compressible fluids filling a bounded domain of three-dimensional space with an infinitely smooth boundary. The boundary condition of slippage without shear stresses is considered. It is proved that the essential spectrum of the problem is a finite set of segments located on the real axis. The discrete spectrum lies on the real axis, with the possible exception of a finite number of complex conjugate eigenvalues. The spectrum of the problem contains a subsequence of eigenvalues with a limit point at infinity and a power-law asymptotic distribution. The asymptotic behavior of solutions to the evolution problem is studied.
Keywords: mixture of fluids, spectral problem, essential spectrum, discrete spectrum, solution asymptotics.
Mots-clés : compressible viscous fluid 
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     author = {D. A. Zakora},
     title = {The problem on small motions of a mixture of viscous compressible fluids},
     journal = {Sibirskie \`elektronnye matemati\v{c}eskie izvesti\^a},
     pages = {1552--1589},
     publisher = {mathdoc},
     volume = {20},
     number = {2},
     year = {2023},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SEMR_2023_20_2_a51/}
}
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D. A. Zakora. The problem on small motions of a mixture of viscous compressible fluids. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 20 (2023) no. 2, pp. 1552-1589. http://geodesic.mathdoc.fr/item/SEMR_2023_20_2_a51/